1. Update on progress with the implementation of a statistical cloud scheme: Prediction of cloud fraction using a PDF- based or “statistical” approach Ben Johnson NCAR: Advanced Study Program / Climate Modeling Section With thanks to: Phil Rasch (NCAR), Adrian Tompkins (ECMWF) & Steve Klein (Lawrence Livermore)

2. Talk outline Cloud fraction methods The Tompkins (2002) cloud scheme Preliminary results from implementation of Tompkins (2002) in NCAR climate model.

3. Why do we need a cloud fraction scheme? The “ All or nothing” approach (if q v > q sat then cloudy, otherwise clear) will not work at GCM resolution! A view of tropical oceanic cloud from space

4. Why is cloud fraction important? Microphysical processes Radiation Cloud fraction LW SW Clear sky Cloud Latent heating

5. Cloud parameterization schemes in GCMs Model State: T,q v,q c,U,V Intermediate model State: T,q v,q c,U,V New model State: T,q v,q c,U,V Cloud fraction scheme Radiation scheme Large-scale condensation & microphysics Convection schemes (deep, shallow) Turbulence scheme (boundary layer, free atmosphere)

6. Current cloud fraction method in CCSM acac RH Mass-flux θ 700mb -θ s a ls a sc Large-scale cloud Convective cloud stratocumulus a total = a(a ls, a sc, a c ) Diagnose cloud fraction based on empirical relationships: (Current method in NCAR CAM) Problems: - No memory - Relationships too simple - a is poorly linked to q c a = cloud fraction Rhcrit = 0.9

7. Motivation for developing a new cloud fraction scheme for CAM Current cloud scheme lacks a solid physical basis and has several deficiencies. The representation of clouds in climate models is one of the biggest sources of uncertainty in climate change projections.

8. Alternative cloud fraction methods 1. Prognostic cloud fraction (Tiedtke 1993) (ECMWF, GFDL) Develop evolution equations for cloud fraction: Model State: T,q v,q c, a,U,V Problems: a is not really a conserved quantity!! Cloud production e.g. Detrainment Cloud dissipation e.g. mixing with dry air -

9. Alternative cloud fraction methods 2. PDF-based or “statistical” schemes (Smith 1990, Tompkins 2002) (Met Office, ECHAM) Construct the PDF of total water (q t ) in a grid box Probability qtqt qsqs CloudyClear Problem: How is the PDF determined? q t = q v + q c

10. How is the PDF determined? 1. Choose a PDF model Aircraft data shows that PDF are usually uni- modal and either gaussian-like, or positively skewed. Tompkins (2002) uses a beta function with three degrees of freedom: mean, variance & skewness. qtqt Positively skewed Symmetric qtqt qtqt

11. How is the PDF determined? 2. Determine the moments The mean (q t ) is given by the model The variance (q t ’ 2 ), and skewness (q t ’ 3 /q t ’ 2 ) are unknown. However, lets think about some possible sources and sinks for variance and skewness in the real world...

12. Processes that create variance and skewness Moist air from convection detrains into dry environment Vertical mixing creates and transports horizontal fluctuations DRY Moist

13. Dissipative mixing reduces variance and skewness Over time horizontal mixing dissipates variance DRY Moist

14. Rain-out reduces variance and skewness Moist anomaly loses moisture via precipitation DRY Moist

15. (1)Production by detrainment of condensate convective updraughts (2)Production by mixing across a gradient (3)Turbulent transport (4)Dissipation (!) or in partially cloudy situations variance can be fitted to q t, q l, and q sat. Prognostic equations for the variance budget (Tompkins 2002) (1) (2) (3) (4)

16. Prognostic equations for the skewness budget (Tompkins 2002) (1) (2) (3) (1)Detrainment of condensate from convective updraughts - K tunable parameter (2) Conversion of condensate into precipitation (microphysics) - Δς closed by assuming no change in lower limit of distribution (3) Dissipation by turbulent mixing - parameterized as newtonian relaxation

17. An alternative method for deriving the variance In partially cloudy situations only, 1. In partially cloudy situations only, the variance can be derived by fitting the PDF to the mean q t and cloud condensate (q c ) predicted by the model, given a certain skewness. In overcast or clear situations prognostic equations must be used to predict variance. Skewness must be prognosed in all situations. Probability qtqt q sat qtqt

18. Intermediate summary A PDF-cloud scheme, based on Tompkins (2002) has been implemented in CAM. What next? Single column model tests Global model tests

19. Single column model tests Forced using a ARM IOP reanalysis data zhang et al. (MWR, 2001) from July 1997 over the Southern Great Plains site. Atmospheric Radiation Measurement (ARM): The Southern Great Plains site (SGP)

20. Single column model test – ARM IOP SGP site July 1997 CAM3: Cloud fraction)

21. Single column model test – ARM IOP SGP site July 1997 CAM3: Cloud fraction with empty clouds removed (where qc is negligible)

22. Single column model test – ARM IOP SGP site July 1997 CAM3: Cloud fraction contribution from large-scale / relative humidity

23. Single column model test – ARM IOP SGP site July 1997 CAM3: Cloud fraction contribution from convective cloud

24. Single column model test – ARM IOP SGP site July 1997 PDF cloud scheme: Cloud fraction

25. Single column model test – ARM IOP SGP site July 1997 CAM3: Cloud fraction with empty clouds removed (where qc is negligible)

26. Single column model test – ARM IOP SGP site July 1997 PDF cloud scheme: Cloud fraction

27. A simplified PDF cloud scheme A simplified version of the Tompkins (2002) Simplifications made: - PDF skewness = 0 - In clear skies PDF width set consistent with critical relative humidity of 0.9 (cloud initiated as relative humidity exceeds 0.9). - If q c > 0 but q v < q sat then partly cloudy, cloud fraction computed by fitting PDF width to be consistent with q c and q v. - If q v = q sat then overcast, cloud fraction = 1, and PDF width such that PDF minimum = q sat.

28. Single column model test – ARM IOP SGP site July 1997 Simplified PDF cloud scheme: Cloud fraction

29. Single column model test – ARM IOP SGP site July 1997 Full PDF cloud scheme: Cloud fraction

30. Conclusions from single column tests Empty clouds occur in CAM, especially associated with convective cloud at mid and low levels. PDF scheme get slightly more high cloud than CAM. Highly simplified PDF scheme gave very similar result to full PDF scheme.

31. Global model tests The simplified PDF cloud scheme has been tested offline (diagnostically) in CAM3.2. Run for 1 year with default climatology for SSTs

32. Annual mean vertically- integrated high high cloud fraction

33. Annual mean vertically- integrated mid-level mid-level cloud fraction

34. Annual mean vertically- integrated low low cloud fraction

35. longwave Annual mean longwave cloud radiative forcing (Wm -2 )

36. shortwave Annual mean shortwave cloud radiative forcing (Wm -2 )

37. Summary chart High cloud fraction Mid-level cloud fraction Low cloud fraction Longwave cloud forcing Shortwave cloud forcing PDF cloud scheme 38.5%17.8%28.6%31.0 Wm -2 -48.8 Wm -2 CAM 337.0%21.5%42.6%30.1 Wm -2 -56.8 Wm -2 PDF scheme - CAM3 1.5%-3.7%-14.0%-0.9 Wm -2 8.0 Wm -2

38. Conclusions from offline global model tests Underestimation of low and mid-level cloud fraction, and shortwave cloud radiative forcing. Slight overestimation of high cloud fraction and longwave cloud radiative forcing.

39. Why such differences / biases? In CAM cloud fraction is completely independent of q c, therefore could still predict moderate cloud even when q c was very small, or even zero (empty clouds). In PDF-based scheme cloud fraction was tied to qc, so would give low cloud fraction when q c was small relative to q sat acac Mass-flux θ 700mb -θ s a sc Convective cloud stratocumulus

40. Why such biases? The non-skewed beta shape used in the simplified PDF scheme is probably a poor approximation. -In upper troposphere one might expect positively skewed PDFs due to cirrus anvils where often we have q c >> q sat -In lower troposphere one might expect negatively skewed PDFs in the lower tropospherre where q c << q sat Upper troposphereLower troposphere q sat More appropriate PDF shapes to use in future tests?

41. Current & future work Explore biases in GCM tests, especially underestimation of low cloud (sensitivity to PDF skewness / shape, and PDF closure methods). Comparison of single column model with ARM and CRM data for specific testcases to develop better understanding of relationships between PDF shape characteristics and atmospheric processes (e.g. Convection, turbulence & microphysics).

42. The end Thanks for your attention!

43. Single column model test – ARM IOP SGP site July 1997 PDF cloud scheme: PDF width / q sat

44. Single column model test – ARM IOP SGP site July 1997 PDF cloud scheme: PDF skewness parameter (PDF is positively skewed when parameter > 2)

45. Prognostic equations for variance budget Moist air detrains into dry envirnoment

46. Prognostic equations for variance budget Vertical mixing across a vertical gradient creates horizontal fluctuations

47. Prognostic equations for variance budget Vertical mixing transports horizontal moisture fluctuations

48. Prognostic equations for variance budget Diffusive horizontal mixing reduces variability in the horizontal turbulence time-scale